Classifying Relations

Abstract

The notion of relations is extremely general and allows for various concepts to be represented. Despite the desirability of having a very abstract notion which is applicable for different concrete systems, more specific notions have the advantage that more properties can be proved about them. This chapter looks at particular classes of relations, enabling the identification and proofs of interesting laws which particular classes of relations satisfy. For instance, one particular class of relations corresponds to the notion of mathematical functions. By focussing only on this class of relations, we can prove results about functions, not all of which may hold for an arbitrary relation. Other classes identified are those of injective, surjective and total relations, applications of which are used in the rest of the book.